An airplane approaches an airport. At a certain time, it is 939 m high. Its angle of elevation measured from the airport is 19.5◦. To the nearest metre, how far is the plane from the airport?
if you want the direct line distance (along the hypotenuse)
sin 19.5 = 939/d
d = 939/sin19.5 = 2813 m
If you want the horizontal displacement
tan 19.5 = 939/x
x = 939/tan19.5 = 2652 m to the nearest metre
Well, isn't this plane in a "high" situation? Here's the deal: We have a right triangle, with the height of the plane being the opposite side and the distance to the airport being the adjacent side. We also have an angle of elevation. So, we can use the tangent function to find the distance. Using some trigonometry magic, the distance to the nearest meter is approximately 2924 meters. Voila! The plane is quite a "distance" away from the airport.
To find the distance between the airplane and the airport, we can use the tangent function.
tan(angle of elevation) = opposite/adjacent
In this case, the opposite side is the height of the airplane (939 m) and the adjacent side is the distance between the airplane and the airport.
Therefore, the equation becomes:
tan(19.5°) = 939 m / adjacent
To find the adjacent side (distance), we can rearrange the equation as follows:
adjacent = 939 m / tan(19.5°)
Using a scientific calculator to find the tangent of 19.5 degrees:
tan(19.5°) = 0.354
Now we can substitute this value back into the equation to find the distance:
adjacent = 939 m / 0.354
adjacent ≈ 2650 m
Therefore, the airplane is approximately 2650 meters away from the airport.
To find the distance between the airplane and the airport, we can use trigonometry. Specifically, we can use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.
Let's label the height of the airplane as "x" and the distance between the airplane and the airport as "d". We can form a right triangle with the hypotenuse being the distance d, the height x being the opposite side, and the horizontal distance being the adjacent side.
Now, we can use the tangent function:
tan(angle) = opposite/adjacent
In this case, we have:
tan(19.5°) = x/d
Rearranging the equation to solve for d:
d = x / tan(19.5°)
Substituting the given height of the airplane (x = 939m) into the equation, we get:
d = 939m / tan(19.5°)
Using a calculator to find the tangent of 19.5°, we find:
tan(19.5°) ≈ 0.351
Now, plugging this value into the equation, we can calculate the distance d:
d = 939m / 0.351 ≈ 2677m
Therefore, to the nearest meter, the plane is approximately 2677 meters away from the airport.